Question

Order of rotational symmetry of a circle is __________.

Answer 1

Step 1: Define rotational symmetry and then find the order of rotational symmetry of a circle.

• Rotation turns an object about a fixed point. This fixed point is the center of rotation.
• The angle by which the object rotates is the angle of rotation. A half-turn means rotation by $180°$; a quarter-turn means rotation by $90°$. Rotation may be clockwise or anticlockwise.
• If, after a rotation, an object looks exactly the same, we say that it has rotational symmetry.
• In a complete turn (of $360°$ ), the number of times an object looks exactly the same is called the order of rotational symmetry.
• The order of symmetry of a square, for example, is $4$ while, for an equilateral triangle, it is $3$.

Step 2: Find the order of rotational symmetry of a circle.

A circle will look exactly the same at an infinite number of points when it rotates $360°$.

Hence the Order of rotational symmetry of a circle is $2$.